The Conway-Maxwell-Poisson distribution: distributional theory and approximation

关于Conway--Maxwell--Poisson分布无穷可分性的评论

Comments on the infinitely divisibility of the Conway--Maxwell--Poisson distribution

本文指出Geng和Xia解决Conway--Maxwell--Poisson分布无穷可分性时使用的复分析方法可被规避，并给出了一个完全初等的证明。

When Is the Conway-Maxwell-Poisson Distribution Infinitely Divisible?

An essential character for a distribution to play a central role in the limit theory is infinite divisibility. In this note, we prove that the Conway-Maxwell-Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or geometric distribution. This explains that, despite its applications in a wide range of fields, there is no theoretical foundation for the CMP distribution to be a natural candidate for the law of small numbers.

On the distributional expansions of powered extremes from Maxwell distribution

In this paper, asymptotic expansions of the distributions and densities of powered extremes for Maxwell samples are considered. The results show that the convergence speeds of normalized partial maxima relies on the powered index. Additionally, compared with previous result, the convergence rate of the distribution of powered extreme from Maxwell samples is faster than that of its extreme. Finally, numerical analysis is conducted to illustrate our findings.

基于Bernstein函数或其逆函数的计数数据模型

On count data models based on Bernstein functions or their inverses

提出一类扩展Conway-Maxwell-Poisson分布的计数数据模型，基于Bernstein及其逆函数，研究其散布性质、阶乘矩表达式，并补充逆函数理论结果。

m-贝尔数与m-斯特林数：迭代二项式变换、超贝塞尔函数及康威-麦克斯韦-泊松分布的矩

$m$-Bell and $m$-Stirling numbers: Iterated binomial transforms, hyper-Bessel functions, and moments of the Conway--Maxwell--Poisson distribution

该研究推广贝尔数得到m-贝尔数，构造m-斯特林三角阵列并证明相关结构定理，还揭示m-贝尔数对应康威-麦克斯韦-泊松分布（ν=m）的矩，拓展了相关数论与概率分布的联系。

Expansions of maximum and minimum from Generalized Maxwell distribution

Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic expansions of joint distribution and density for normalized partial maxima and minima are established. These expansions are used to educe speeds of convergence of joint distribution and density of normalized maxima and minima tending to its corresponding ultimate limits. Numerical analysis are provided to support our results.